We construct a minimal two-chain random walk model and study the information that fluctuations of the flux and higher cumulants can reveal about the model: its structure, parameters, and whether it operates under nonequilibrium conditions. The two coupled chains allow for both horizontal and cyclic transport. We capture these processes by deriving the cumulant generating function of the system, which characterizes both horizontal and cyclic transport in the long time limit. First, we show that either the horizontal or the cyclic currents, along with their higher-order cumulants, can be used to unravel the intrinsic structure and parameters of the model. Second, we investigate the “zero current” situation, in which the horizontal current vanishes. We find that fluctuations of the horizontal current reveal the nonequilibrium condition at intermediate bias, while the cyclic current remains nonzero throughout. We also show that in nonequilibrium scenarios close to the zero horizontal current limit, the entropy production rate is more tightly lower-bounded by the relative noise of the cyclic current, and vice versa. Finally, simulations of transport before the steady state sets in allow for the extraction of the interchain hopping rate. Our study, illustrating the information concealed in fluctuations, could see applications in chemical networks, cellular processes, and charge and energy transport materials.

We discuss a one-dimensional coupled qubit-array quantum battery model under Born-Karman boundary conditions and investigate both the charging and discharging processes. Applying the stored energy, charging power, and ergotropy as the essential physical indicators of quantum battery, it is observed that minimizing the hopping interaction between the nearest-neighbor qubits in the qubit-array and increasing the number of qubits during battery setup are crucial. Additionally, we employ a classical driving field to optimize battery performance and explore the optimal quantum battery performance by adjusting the driving strength of the classical field. Finally, we have discovered that the initial energy in the charger no longer needs to be higher than the energy in the battery in our protocol, the charger will continue to supply energy to the battery even when there is limited initial available energy in the charger. And the conventional approach of preparing the battery's initial state in its ground state, as observed in previous studies, may not necessarily be the optimal choice. By introducing a strong classical driving field, it is possible to enhance energy storage by allowing for an initial presence of some energy within the battery.

We introduce a perspective that has not appeared before in the field of equal and multifrequency coupling derived from considering neuronal synchrony as a possible equivalence relation. The experimental results agree with the theoretical prediction that cross-frequency coupling results in a partition of the brain synchrony state space. We place these results in the framework of the integration and segregation of information in the processing of sensorimotor transformations by the brain cell circuits and propose that equal-frequency (1:1) connectivity favors integration of information in the brain whereas cross-frequency coupling (n:m) favors segregation. These observations may provide an outlook about how to reconcile the need for stability in the brain's operations with the requirement for diversity of activity in order to process many sensorimotor transformations simultaneously.

The dynamics of a voltage-gated potassium channel in real environments represents a crucial bridge between its molecular structure and functions. However, it is still missing due to the mathematical difficulty that arises from the high dimensionality and nonlinear interregulation. Here we present a method for solving the stationary distribution of a hybrid process that contains two negatively interregulating kinetics: channel gating and voltage decay. The results can be summarized as follows: first, the voltage distribution is determined by the competition of their time scales; second, the fluctuation structures in parameter space illustrate that, to perform the voltage-controlling task, the channel gating is elastic while the membrane produces the stabilizing function; third, the power dissipated by the capacitive currents and the internal battery current are calculated and explained. Based on these findings, we examine the manner in which macroscopic functions of potassium channels are manifested. Our methodology provides an accurate characterization of hybrid processes that are pervasive in the life sciences.

We demonstrate that the update of weight matrices in learning algorithms can be described in the framework of Dyson Brownian motion, thereby inheriting many features of random matrix theory. We relate the level of stochasticity to the ratio of the learning rate and the minibatch size, providing more robust evidence to a previously conjectured scaling relationship. We discuss universal and nonuniversal features in the resulting Coulomb gas distribution and identify the Wigner surmise and Wigner semicircle explicitly in a teacher-student model and in the (near-)solvable case of the Gaussian restricted Boltzmann machine.

Steady-state currents generically occur both in systems with continuous translation invariance and in nonequilibrium settings with particle drift. In either case, thermal fluctuations advected by the current act as a source of noise for slower hydrodynamic modes. This noise is unconventional, since it is highly correlated along spacetime rays. We argue that, in quasi-one-dimensional geometries, the correlated noise from ballistic modes generically gives rise to anomalous full counting statistics (FCS) for diffusively spreading charges. We present numerical evidence for anomalous FCS in two settings: (1) a two-component continuum fluid and (2) the totally asymmetric exclusion process initialized in a nonequilibrium state.

We show that the conventional Jarzynski equality does not hold for a system prepared in a microcanonical ensemble. We derive a modified equality that connects microcanonical work fluctuations to entropy production, in an analogous way to the Jarzynski equality, but with reference to an inverse temperature that depends on the path of the work protocol. For close to isothermal processes the modified equality can improve on the bound $\langle W\rangle \ge \mathrm{\Delta }F$. Our result is a special case of a general expression for the microcanonical moment-generating function for any extensive quantity, which enables calculation of the breakdown of ensemble equivalence for thermodynamic fluctuations. We demonstrate our microcanonical Jarzynski equality in a system of driven two-level spins.

Collisional models, or repeated interaction schemes, are a category of microscopic open quantum system models that have seen growing use in studying quantum thermalization, in which the bath is modeled as a large ensemble of identical ancillas that sequentially interact with the system. We demonstrate an equivalence between the system dynamics generated by the collisional model framework and the Metropolis algorithm, subject to two primary conditions. Namely, that each collisional model bath ancilla is prepared in a thermal state with a discrete spectrum that matches the energy eigenstate transitions of the system and that the ratio of the ancilla partition function to the number of system eigenstates remains small. If these conditions are satisfied, then the system dynamics generated by both methods are identical for arbitrary initial states and in both the steady-state and transient regimes. This allows the typically purely phenomenological Metropolis scheme to be used as a tool to study exact prethermalization dynamics without the need to explicitly model the system-bath interaction.

We investigate the behavior of heat conduction in two-dimensional (2D) electron gases without and with a magnetic field. We perform simulations with the multiparticle collision approach, suitably adapted to account for the Lorenz force acting on the particles. For zero magnetic field, we find that the heat conductivity $\kappa$ diverges with the system size $L$ following the logarithmic relation $\kappa \sim lnL$ (as predicted for 2D systems) for small $L$ values; however, in the thermodynamic limit the heat conductivity tends to follow the relation $\kappa \sim L^{1/3}$, as predicted for one-dimensional (1D) fluids. This suggests the presence of a dimensional-crossover effect in heat conduction in electronic systems that adhere to standard momentum conservation. Under the magnetic field, time-reversal symmetry is broken and the standard momentum conservation in the system is no longer satisfied but the pseudomomentum of the system is still conserved. In contrast with the zero-field case, both equilibrium and nonequilibrium simulations indicate a finite heat conductivity independent on the system size $L$ as $L$ increases. This indicates that pseudomomentum conservation can exhibit normal diffusive heat transport, which differs from the abnormal behavior observed in low-dimensional coupled charged harmonic oscillators with pseudomomentum conservation in a magnetic field. These findings support the validity of the hydrodynamic theory in electron gases and clarify that pseudomomentum conservation is not enough to ensure the anomalous behavior of heat conduction.

A pointlike particle diffusing in a two-dimensional channel is considered. Its width $h(x,t)$ varies not only with the longitudinal coordinate $x$, but also in time $t$. Reducing the transverse degree of freedom in the corresponding diffusion equation, we arrive at the effective one-dimensional dynamics along the channel, represented by the generalized Fick-Jacobs equation; its coefficients calculated recursively also depend on time. In contrast to the static confinement, the moving boundaries generate an effective force driving the particle in the channel, which can be explicitly expressed within our method. We analyze this force in two examples: deformation of the boundary advancing as the traveling wave and in the channel “breathing” with an amplitude varying in $x$.

Swarmalators are entities that combine the swarming behavior of particles with the oscillatory dynamics of coupled phase oscillators and represent a novel and rich area of study within the field of complex systems. Unlike traditional models that treat spatial movement and phase synchronization separately, swarmalators exhibit a unique coupling between their positions and internal phases, leading to emergent behaviors that include clustering, pattern formation, and the coexistence of synchronized and desynchronized states, etc. This paper presents a comprehensive analysis of a two-dimensional swarmalator model in the presence of a predatorlike agent that we call a contrarian. The positions and the phases of the swarmalators are influenced by the contrarian and we observe the emergence of intriguing collective states. We find that swarmalator phases are synchronized even with negative coupling strength when their interaction with the contrarian is comparatively strong. Through a combination of analytical methods and simulations, we demonstrate how varying these parameters can lead to transitions between different collective states.

Quantum channels describe subsystem or open-system evolution. Using the classical Koopman operator that evolves functions on phase space, four classical Koopman channels are identified as analogs of the four possible quantum channels in a bipartite setting. Thus, when the complete evolution has a quantum-classical correspondence, the correspondence at the level of the subunitary channels can be studied. The channels, both classical and quantum, can be interpreted as noisy single-particle systems. Having parallel classical and quantum operators gives us new access to study the fine details of these major limiting theories. Using a coupled kicked rotor as a generic example, we contrast and compare spectra of the quantum and classical channels. The largest nontrivial mode of the quantum channel is seen to be mostly determined by the stable parts of the classical phase space, even those that are surprisingly small relative to the scale of an effective $\hslash$. In cases where the dynamics have a significant fraction of chaos, the spectrum exhibits a prominent annular density, which is approximately described by the single-ring theorem of random matrix theory. The ring shrinks in size when the classical limit is approached. However, the eigenvalues and modes that survive the classical limit appear to be scarred by unstable manifolds or, if they exist, stable periodic orbits.

In our previous paper [N. Tsutsumi et al., Chaos 32, 091101 (2022)], we proposed a method for constructing a system of differential equations of chaotic behavior from only observable deterministic time series, which we call the radial function-based regression (RfR) method. However, when the targeted variable's behavior is rather complex, the direct application of the RfR method does not function well. In this study, we propose a method of modeling such dynamics, including the high-frequency intermittent behavior of a fluid flow, by considering another variable (base variable) showing relatively simple, less intermittent behavior. We construct an autonomous joint model composed of two parts: the first is an autonomous system of a base variable, and the other concerns the targeted variable being affected by a term involving the base variable to demonstrate complex dynamics. The constructed joint model succeeded in not only inferring a short trajectory but also reconstructing chaotic sets and statistical properties obtained from a long trajectory such as the density distributions of the actual dynamics.

Synchronization of nonlinear systems is a crucial problem in many applications, including system identification, data forecasting, compressive sensing, coupled oscillator topologies, and neuromorphic systems. Despite many efficient synchronization techniques being developed, there are some unresolved issues such as fast and reliable synchronization using short or noisy fragments of available data. In this paper, we use time-reversible integration to obtain a synchronization technique as a generalization of the well-known Pecora-Carroll method. The proposed time-symmetric synchronization technique employs the time reversibility of a discrete system obtained by the symmetric integration method. This approach allows the complete synchronization of two chaotic systems using minimal, sparse, or noisy sync data from one state variable without any controller. An example of rapid unidirectional time-symmetric synchronization of several test chaotic systems is shown to verify the performance of the proposed technique. We show that the time-reversible approach works for both conservative and dissipative systems, but highly depends on initial conditions. To increase the overall performance of the time-symmetric synchronization scheme, we suggest using a computationally simple and easy-to-implement time-reversible semi-implicit numerical integration method. Several possible applications include chaos-based communications, chaotic signal filtering, and systems based on coupled oscillators.

The phenomenon of branched flow, visualized as a chaotic arborescent pattern of propagating particles, waves, or rays, has been identified in disparate physical systems ranging from electrons to tsunamis, with periodic systems only recently being added to this list. Here, we explore the laws governing the evolution of the branches in periodic potentials. On one hand, we observe that branch formation follows a similar pattern in all nonintegrable potentials, no matter whether the potentials are periodic or completely irregular. Chaotic dynamics ultimately drives the birth of the branches. On the other hand, our results reveal that for periodic potentials the decay of the branches exhibits new characteristics due to the presence of infinitely stable branches known as superwires. Again, the interplay between branched flow and superwires is deeply connected to Hamiltonian chaos. In this work, we explore the relationships between the laws of branched flow and the structures of phase space, providing extensive numerical and theoretical arguments to support our findings.

Mutually beneficial interactions between plants and pollinators are crucial for biodiversity, ecosystem stability, and crop production. A threat to a mutualistic network is the occurrence of a tipping point at which the species abundances collapse to a near zero level. In modern agriculture, there is widespread use of pesticides. What are the effects of extensive pesticide use on mutualistic networks? We develop a plant-pollinator-pesticide model and study its dynamics using 123 mutualistic networks across the globe. We demonstrate that pesticide exposure can lead to a tipping point. Furthermore, while the network characteristics such as richness and modularity exhibit a strong association with pesticide-induced tipping, nestedness shows a weak association. A surprising finding is that the mutualistic networks in the African continent are less pesticide tolerant than those in Europe. We articulate and test a pragmatic intervention strategy through targeted management of pesticide levels within specific plant species to delay or avert the tipping point. Our study provides quantitative insights into the phenomenon of pesticide-induced tipping for safeguarding mutualistic networks that are fundamental to agriculture and ecosystems.

The well-known Navier-Stokes-Fourier equations of fluid dynamics are, in general, not adequate for describing rarefied gas flows. Moreover, while the Stokes equations—a simplified version of the Navier-Stokes-Fourier equations—are effective in modeling slow and steady liquid flow past a sphere, they fail to yield a nontrivial solution to the problem of slow and steady liquid flow past an infinitely long cylinder (a two-dimensional problem essentially); this is referred to as Stokes' paradox. The paradox also arises when studying these problems for gases. In this paper, we present a way to obtain meaningful solutions for two-dimensional flows of rarefied gases around objects by circumventing Stokes' paradox. To this end, we adopt an extended hydrodynamic model, referred to as the CCR model, consisting of the balance equations for the mass, momentum, and energy and closed with the coupled constitutive relations. We determine an analytic solution of the CCR model for the problem and compare it with a numerical solution based on the method of fundamental solutions. Apart from addressing flow past a circular cylinder, we aim to showcase the capabilities of the method of fundamental solutions to predict the flow past other objects in two dimensions for which analytic solutions do not exist or are difficult to determine. For that, we investigate the problem of rarefied gas flow past an infinitely long semicircular cylinder.

The intrinsic bulk viscosity of the one-component plasma (OCP) is computed and analyzed using equilibrium molecular dynamics simulations and the Green-Kubo formalism. It is found that bulk viscosity exhibits a maximum at $\mathrm{\Gamma }\approx 1$, corresponding to the condition that the average kinetic energy of particles equals the potential energy at the average interparticle spacing. The weakly coupled and strongly coupled limits are analyzed and used to construct a model that captures the full range of coupling strengths simulated: $\mathrm{\Gamma }\approx {10}^{-2}\text{–}{10}^2$. Simulations are also run of the Yukawa one-component plasma (YOCP) in order to understand the impact of electron screening. It is found that electron screening leads to a smaller bulk viscosity due to a reduction in the excess heat capacity of the system. Bulk viscosity is shown to be at least an order of magnitude smaller than shear viscosity in both the OCP and YOCP. The generalized frequency-dependent bulk viscosity coefficient is also analyzed. This is found to exhibit a peak near twice the plasma frequency in strongly coupled conditions, which is associated with the oscillatory decay observed in the bulk viscosity autocorrelation function. The generalized shear and bulk viscosity coefficients are found to have a similar magnitude for $\omega \gtrsim 2{\omega }_p$ at strongly coupled conditions.